Gradient-index glass is often made in the form of solid cylindrical bodies. The index of such bodies changes radially, usually with the highest index being along the axis of the cylinder and the lowest index located at the outer periphery.
Generally, the profile of a radial gradient-index glass can be mathematically expressed in terms of the following formula: EQU n=N.sub.00 +N.sub.10 r.sup.2 +N.sub.20 r.sup.4. . . ,
where:
n is the refractive index, PA0 r is the radial distance from the axis of the glass to its periphery, and PA0 N.sub.00, N.sub.10, and N.sub.20 are constants.
Parabolic gradient profile shapes are particularly desirable for gradient-index glass used in lenses, and, for such configurations, the above formula simplifies to the following: EQU n=N.sub.00 +N.sub.10 r.sup.2.
In defining the profile shape of gradient index glass, the N.sub.10, .DELTA.n, and % .DELTA.n due to N.sub.10 (i.e., (N.sub.10 r.sup.2.sub.periphery /.DELTA.n).times.100) parameters are particularly important. .DELTA.n is defined as the difference between the refractive index at the periphery and the axis of the glass. For a parabolic glass configuration, .DELTA.n is N.sub.10 (r.sup.2.sub.periphery.sup.- r.sup.2.sub.axis), where r.sub.axis is zero. The optical power contributed by gradient index glass is dictated by the value of N.sub.10, with N.sub.10 values less than 0 indicating a positive optical power. The more negative N.sub.10 is, the more positive optical power is introduced. The %.DELTA.n due to the N.sub.10 term is a primary indicator of the parabolic character of a particular gradient index glass. As the %.DELTA.n due to the N.sub.10 term approaches 100%, the particular glass assumes a more parabolic configuration.
The use of gradient index glass in optical elements provides many advantages over homogeneous glass bodies in which the index is constant. For example, a single gradient-index glass element provides the performance of multiple element lenses and reduces the volume of the body. The applications for gradient index glass have, however, been limited by the lack of suitable materials and of suitable production techniques. For example, the limitations of ion exchange processes relate to size, environmental and thermal stability, index profile dispersion, base index (i.e., N.sub.00), and maximum .DELTA.n.
Historically, gradient index glass has been made with silicate preforms. See, e.g., U.S. Pat. Nos. 3,938,974 and 4,302,231. These preforms are fabricated either by leaching a phase separated glass or by sol gel methods.
Such techniques involve creating and then fixing into place a concentration gradient of refractive index modifying dopants within the porous preform. The preform is then dried and heated until it becomes a pore-free glass element with an index gradient. The sol gel and other techniques are reviewed in U.S. Pat. No. 4,686,195 to Yamane.
Gradient index glass prepared by diffusion in inorganic oxide gel monoliths is proposed by Mukherjee, S.P., "Gradient Index Lens Fabrication Processes: A Review, in Topical Meeting on Gradient-Index Optical Imaging Systems," Honolulu, Hi., Optical Society of America (1981), pages Tu Al 1 to Tu Al 5. This paper identifies the following potential advantages of using sol gel precursors in the production of gradient index glass: (1) relatively large diffusion coefficients; (2) low energy consumption during most the process; and (3) the ability to introduce a broad variety of index modifying dopants into the sol-gel preform.
U.S. Pat. No. 4,686,195 to Yamane produces gradient index glass by a sol-gel technique. This technique involves mixing a silicon alkoxide with water, a source of boron oxide, and an aqueous metal salt solution which is the source of modifier cations. This mixture forms a gel which then is placed in a solution to leach out some of the metal salts contained within it and to have other metal salts introduced into it by diffusion. The gel is then dried and sintered into glass. M. Yamane et. al, "Gradient-Index Glass Rods of PbO.multidot.K.sub.2 O.multidot.B.sub.2 O.sub.3 .multidot.SiO.sub.2 System Prepared by the Sol Gel Process," JournaI of Non Crystalline Solids, 100, 506-10 (1988) discloses a similar process in which the concentration gradient index of cations is fixed by a reprecipitation mechanism in acetone or iso propanol.
Shingyouchi et. al., Electronics Letters, 22:99 100, 1108-1110 (1986), utilizes germanium alkoxide as the index modifying cation. The index modifier is thus fully incorporated into the gel structure, and the index profile does not suffer from uncontrollable asymmetry.
First, tetramethoxy silane (a silicon alkoxide) is combined with tetraethoxy germanium (a germanium alkoxide), ethanol, water, and hydrochloric acid. The mixture forms a gel which is placed in water to leach out some of the germanium component. The gel is then washed in methanol to fix the germanium concentration gradient, dried, and sintered into gradient index glass. Shingyouchi el. al. also uses titanium to replace germanium as the index modifying cation. The resulting glass is a 2mm diameter rod with a .DELTA.n of 0.013.
The method of Shingyouchi et. al. involves the use of only two components: silica and an index modifying oxide, such as germanium dioxide or titanium dioxide. The method can be generalized to substitute zirconium dioxide as well. These binary systems, however, yield gels with decreased porosity, making them difficult to dry and sinter without fracturing or bloating. The SiO.sub.2 .multidot.TiO.sub.2 binary system tends to crystallize at elevated temperatures if the TiO.sub.2 content tends to bloat at elevated temperatures, because the outside portions of the gel collapse before the inside portions, thereby trapping any released gases.
U.S. Pat. Nos. 4,797,376 and 4,902,650 to Caldwell et al. disclose a sol gel method for producing gradient index glass in a ternary system. This process is initiated by forming a mixture of silicon alkoxide and alcohol in an aqueous solution sufficiently acidic to hydrolyze partially the silicon alkoxide. An index modifying metal alkoxide, an additional metal alkoxide, and water are then added to the mixture. This converts the metal alkoxides to a network of corresponding metal oxides suitable for gelation. A gel is then formed by molding the mixture containing the network of metal oxides. The gel is acid leached, fixed in alcohol, dried, and sintered to a transparent gradient index glass. U.S. Pat. No. 5,068,208 to Haun, et al. discloses the use of water or a mixture of water and alcohol as fixing agents in such processes.
In the processes disclosed by U.S. Pat. Nos. 4,797,376 and 4,902,650 to Caldwell, et al. and U.S. Pat. No. 5,068,208 to Haun, et al., the alkoxide mixture typically includes alkoxides of silicon, aluminum, and titanium. When the resulting gel is leached with a strong acid, both the aluminum structure modifier and the titanium index modifier are removed simultaneously. The glass ultimately produced has been deficient, because the presence of the aluminum during the removal of the titanium alters the manner in which the titanium is removed. This can adversely affect the final an or profile shape. The process of the present invention is directed to overcoming such deficiencies.